Game with piles of stones
Source: St Petersburg 2022 9.5~10.4
September 28, 2022
combinatorics
Problem Statement
There are two piles of stones: stones in one pile and in the other. Sasha and Olya
play the game, making moves in turn, Sasha starts. Let before the player's move the heaps contain and stones, with . Then, on his own move, the player is allowed take from the pile with stones any number of stones from to . A player loses if he can't make a move. Who wins?Remark: For 10.4, the initial numbers are